The harmonics are different with every rifle.
As was said, the idea is to get the barrel to move as far as the harmonics are concerned the same way every time. There are tuners, put on the end of the barrel, adjustable to change the weight and the way the barrel moves. Tuners put on the middle part of the barrel.
Look up Rimfireaccuracy site, there is a lot of talk about barrels and the harmonics there.
Call Shilen barrels, the guy that owns the company will most likely talk to you about it. He's a custom barrel manufactuer.
Barrel harmonics is an inexact science, we know that every barrel has it's own harmonics and has to be tuned for the best accuracy. In other words, if it whips upward, it needs to whip upward the same for every shot. Change anything, bullet, bullet weight, the way the rifle is held and you will change the harmonics and need to start over.
The heavier the barrel, the less movement, but every barrel has harmonics.
Go to www.brownells.com
, they have a book by a guy named Pope, he was one of the best barrel makers ever. He is long gone, but the book should contain a lot of info. Also get "Understanding Firearms Ballistics" by Robert Rinker. There are things about barrels in the book and you need to understand ballistics to help understand what barrels do. This book will help. Easy to read, some math you can work out. If you have trouble find them on the web site, call, they will find it for you. If they don't have the books, go to www.midwayusa.com
I'm a retired Gunsmith and have had to try everything to get the harmonics right on some guns. Each is different. It's not easy and requires a lot of expermintation and a lot of shot ammo sometimes to get it right. Most people don't get into this extream accuracy except for comp shooters. They have and will try anything if it's within the rules and makes their rifles shoot better.
Just getting an adjustable tuner perfect can use 500 rounds of ammo sometimes. You picked an interesting subject. The two books I suggested should help. I have not read the book by Pope, but it should give some more understanding.
Also, not every barrel whips like the AK-47, it is the extream rifle for barrel whip.
Good luck, John K